Question

Find all trigonometric functions of angle in standard position whose terminal arm passes through point (3, −4).

Answer 1

Let θ be the measure of the angle in standard position whose terminal arm passes through P(3, – 4).

∴ x = 3 and y = - 4

r = OP

∴ r = `sqrt((3 - 0)^2 + (- 4 - 0)^2)`

= `sqrt(9 + 16)`

= 5

∴ sin θ = `y/"r" = - 4/5`

cos θ = `x/"r" = 3/5`

tan θ = `y/x = (-4)/3 = -4/3`

cosec θ = `"r"/y = 5/(-4) = -5/4`

sec θ = `"r"/x = 5/3`

cot θ = `x/y = 3/(-4) = -3/4`